The usual examples of Lagrange point mechanics one most commonly encounters, Sun-Earth-L# and Earth-Moon-L#, are examples of 3-body problems where 1 >> 2 >> 3 in terms of their mass. The Pluto-Charon system, however, are much closer in their relative masses, so much so that their barycenter is outside Pluto's surface. From the wiki:
Pluto and Charon are sometimes described as a binary system because the barycenter of their orbits does not lie within either body.[23] The IAU has yet to formalise a definition for binary dwarf planets, and Charon is officially classified as a moon of Pluto.[24]
How does this affect the orbital stability of the 5 PCL points?
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